Question

ABCD dreptunghi cu BD=26cm si sin(unghiul DBC)= 5/13. Aflati perimetrul si aria dreptunghiului.

Answer 1

ΔDCB,mas<C=90
sin<B=5/13
sin<B=DC/DB     5/13=DC/26   ⇒DC=5*26/13= 5*2=10
BC²=DB²-DC²=26²-10²=676-100=576   ⇒BC=24
P=2L+2l=2*24+2*10=48+20=68
A=L*l=24*10=240

Answer 2

ABCD- dreptunghi,  AB=CD-latimea dreptunghiului,BC=AD-lungimea dreptunghiului
BD=AC-diagonala dreptunghiului=26 cm, sin(DBC)=5/13
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P=?
A=?
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In tr DBC  sin(ung DBC)=5/13=> sin(ung DBC)=DC/DB=>5/13=DC/26=>DC=26*5/13=10 cm, iar in acelasi tr BC²=DB²-DC²=676-100=576=24²=>BC=24 cm
P=2L+2l=2*24+2*10=48+20=68 cm
A=L*l=24*10=240 cm, unde L-lungime,l-latime,P-perimetrul dreptunghiului A-aria dreptunghiului